Slash.Wang’s project 2
所选项目：红葡萄酒质量
1. 初始化数据
## X fixed.acidity volatile.acidity citric.acid
## Min. : 1.0 Min. : 4.60 Min. :0.1200 Min. :0.000
## 1st Qu.: 400.5 1st Qu.: 7.10 1st Qu.:0.3900 1st Qu.:0.090
## Median : 800.0 Median : 7.90 Median :0.5200 Median :0.260
## Mean : 800.0 Mean : 8.32 Mean :0.5278 Mean :0.271
## 3rd Qu.:1199.5 3rd Qu.: 9.20 3rd Qu.:0.6400 3rd Qu.:0.420
## Max. :1599.0 Max. :15.90 Max. :1.5800 Max. :1.000
## residual.sugar chlorides free.sulfur.dioxide
## Min. : 0.900 Min. :0.01200 Min. : 1.00
## 1st Qu.: 1.900 1st Qu.:0.07000 1st Qu.: 7.00
## Median : 2.200 Median :0.07900 Median :14.00
## Mean : 2.539 Mean :0.08747 Mean :15.87
## 3rd Qu.: 2.600 3rd Qu.:0.09000 3rd Qu.:21.00
## Max. :15.500 Max. :0.61100 Max. :72.00
## total.sulfur.dioxide density pH sulphates
## Min. : 6.00 Min. :0.9901 Min. :2.740 Min. :0.3300
## 1st Qu.: 22.00 1st Qu.:0.9956 1st Qu.:3.210 1st Qu.:0.5500
## Median : 38.00 Median :0.9968 Median :3.310 Median :0.6200
## Mean : 46.47 Mean :0.9967 Mean :3.311 Mean :0.6581
## 3rd Qu.: 62.00 3rd Qu.:0.9978 3rd Qu.:3.400 3rd Qu.:0.7300
## Max. :289.00 Max. :1.0037 Max. :4.010 Max. :2.0000
## alcohol quality
## Min. : 8.40 Min. :3.000
## 1st Qu.: 9.50 1st Qu.:5.000
## Median :10.20 Median :6.000
## Mean :10.42 Mean :5.636
## 3rd Qu.:11.10 3rd Qu.:6.000
## Max. :14.90 Max. :8.000##
## 0.99007 0.9902 0.99064 0.9908 0.99084 0.9912 0.9915 0.99154 0.99157
## 2 1 2 1 1 1 1 1 1
## 0.9916 0.99162 0.9917 0.99182 0.99191 0.9921 0.9922 0.99235 0.99236
## 2 1 1 2 1 1 2 1 1
## 0.9924 0.99242 0.99252 0.99256 0.99258 0.99264 0.9927 0.9928 0.99286
## 3 2 1 1 3 1 1 2 1
## 0.9929 0.99292 0.99294 0.99306 0.99314 0.99316 0.99318 0.9932 0.99322
## 1 1 2 1 1 2 1 1 1
## 0.99323 0.99328 0.9933 0.99331 0.99332 0.99334 0.99336 0.9934 0.99341
## 1 1 1 2 1 1 1 4 1
## 0.99344 0.99346 0.99348 0.9935 0.99352 0.99354 0.99356 0.99357 0.99358
## 1 3 1 1 2 2 4 1 3
## 0.9936 0.99362 0.99364 0.9937 0.99371 0.99374 0.99376 0.99378 0.99379
## 2 2 1 2 2 2 3 3 1
## 0.9938 0.99384 0.99385 0.99386 0.99387 0.99388 0.99392 0.99394 0.99395
## 1 1 1 1 1 2 2 1 1
## 0.99396 0.99397 0.994 0.99402 0.99408 0.9941 0.99414 0.99416 0.99417
## 3 1 2 4 3 1 2 1 1
## 0.99418 0.99419 0.9942 0.99425 0.99426 0.99428 0.9943 0.99434 0.99437
## 2 2 3 1 1 1 2 1 1
## 0.99438 0.99439 0.9944 0.99444 0.99448 0.99451 0.99454 0.99456 0.99458
## 5 1 3 4 4 1 1 1 4
## 0.99459 0.9946 0.99462 0.99464 0.99467 0.99468 0.9947 0.99471 0.99472
## 1 5 2 2 2 1 6 3 3
## 0.99473 0.99474 0.99476 0.99478 0.99479 0.9948 0.99483 0.99484 0.99486
## 1 1 3 2 1 9 1 3 1
## 0.99488 0.99489 0.9949 0.99491 0.99492 0.99494 0.99495 0.99496 0.99498
## 4 3 4 1 2 4 2 1 5
## 0.99499 0.995 0.99501 0.99502 0.99504 0.99506 0.99508 0.99509 0.9951
## 1 10 1 2 2 1 3 1 4
## 0.99512 0.99514 0.99516 0.99517 0.99518 0.99519 0.9952 0.99521 0.99522
## 2 5 6 1 3 1 9 1 4
## 0.99523 0.99524 0.99525 0.99526 0.99528 0.99529 0.9953 0.99531 0.99532
## 1 4 2 2 3 1 4 2 1
## 0.99533 0.99534 0.99536 0.99538 0.9954 0.99541 0.99542 0.99543 0.99544
## 1 6 2 11 4 1 1 2 1
## 0.99545 0.99546 0.99547 0.99549 0.9955 0.99551 0.99552 0.99553 0.99554
## 3 7 2 2 14 3 5 1 3
## 0.99555 0.99556 0.99557 0.99558 0.9956 0.99562 0.99564 0.99565 0.99566
## 1 2 3 3 14 4 2 3 4
## 0.99568 0.99569 0.9957 0.99572 0.99573 0.99574 0.99575 0.99576 0.99577
## 4 1 6 9 1 2 2 5 3
## 0.99578 0.9958 0.99581 0.99582 0.99584 0.99585 0.99586 0.99587 0.99588
## 3 14 1 1 2 3 6 2 4
## 0.99589 0.9959 0.99592 0.99593 0.99594 0.99596 0.99598 0.99599 0.996
## 1 13 4 2 1 2 2 2 13
## 0.99603 0.99604 0.99605 0.99606 0.99608 0.99609 0.9961 0.99612 0.99613
## 2 3 3 2 2 1 10 6 4
## 0.99614 0.99615 0.99616 0.99617 0.99619 0.9962 0.99621 0.99622 0.99623
## 2 5 7 1 1 28 1 5 2
## 0.99624 0.99625 0.99627 0.99628 0.99629 0.9963 0.99631 0.99632 0.99633
## 3 3 3 3 2 15 1 4 4
## 0.99634 0.99635 0.99636 0.99638 0.99639 0.9964 0.99641 0.99642 0.99643
## 3 1 5 5 2 25 1 3 1
## 0.99645 0.99646 0.99647 0.99648 0.99649 0.9965 0.99651 0.99652 0.99654
## 1 1 2 3 1 11 1 6 2
## 0.99655 0.99656 0.99658 0.99659 0.9966 0.99661 0.99664 0.99665 0.99666
## 6 5 1 2 23 1 3 1 3
## 0.99667 0.99668 0.99669 0.9967 0.99672 0.99674 0.99675 0.99676 0.99677
## 1 4 2 13 5 2 5 3 2
## 0.99678 0.9968 0.99682 0.99683 0.99684 0.99685 0.99686 0.99688 0.99689
## 1 35 2 2 1 8 3 2 4
## 0.9969 0.99692 0.99693 0.99694 0.99695 0.99697 0.99698 0.99699 0.997
## 18 4 2 3 1 1 1 1 24
## 0.99701 0.99702 0.99704 0.99705 0.99706 0.99708 0.99709 0.9971 0.99712
## 2 4 3 1 2 4 1 13 4
## 0.99713 0.99714 0.99716 0.99717 0.99718 0.99719 0.9972 0.99721 0.99722
## 2 2 2 1 3 1 36 1 1
## 0.99724 0.99725 0.99726 0.99727 0.99728 0.99729 0.9973 0.99732 0.99733
## 4 1 1 1 3 1 18 3 1
## 0.99734 0.99735 0.99736 0.99738 0.99739 0.9974 0.99743 0.99744 0.99745
## 4 6 5 4 1 22 2 2 9
## 0.99746 0.99747 0.99748 0.9975 0.99752 0.99754 0.99756 0.99758 0.9976
## 7 2 3 7 1 1 1 1 35
## 0.99761 0.99764 0.99765 0.99768 0.99769 0.9977 0.99772 0.99774 0.99779
## 1 1 1 3 2 4 1 5 1
## 0.9978 0.99782 0.99783 0.99784 0.99785 0.99786 0.99787 0.99788 0.9979
## 26 2 2 1 1 4 3 2 14
## 0.99791 0.99796 0.99798 0.998 0.99801 0.99803 0.99808 0.9981 0.99814
## 1 1 2 29 2 3 1 10 2
## 0.99815 0.99817 0.99818 0.9982 0.99822 0.99823 0.99824 0.99828 0.9983
## 2 2 3 23 1 1 3 2 9
## 0.99832 0.99834 0.99836 0.9984 0.99842 0.99845 0.9985 0.99852 0.99854
## 1 1 2 20 2 1 3 1 1
## 0.99855 0.99859 0.9986 0.99864 0.99865 0.9987 0.99878 0.9988 0.99888
## 2 1 19 1 2 12 1 20 2
## 0.9989 0.99892 0.999 0.99901 0.9991 0.99914 0.99915 0.99918 0.9992
## 2 3 8 1 10 3 1 1 7
## 0.99922 0.99925 0.9993 0.99935 0.99938 0.99939 0.9994 0.9995 0.9996
## 1 1 4 1 1 1 24 1 12
## 0.99965 0.9997 0.99974 0.99975 0.99976 0.9998 0.9999 1 1.00005
## 1 8 1 1 1 10 1 10 2
## 1.0001 1.00012 1.00015 1.0002 1.00024 1.00025 1.0003 1.0004 1.0006
## 4 1 2 10 1 1 2 9 6
## 1.0008 1.001 1.0014 1.0015 1.0018 1.0021 1.0022 1.00242 1.0026
## 3 6 6 2 1 2 2 2 2
## 1.00289 1.00315 1.0032 1.00369
## 1 3 1 2##
## 3 4 5 6 7 8
## 10 53 681 638 199 18密度变化较为分散；大部分酒的质量集中在5,6左右。在fixed.acidity，volatile.acidity, citric.acid, residual.sugar,chlorides, free.sulfur.dioxide, total.sulfur.dioxide中，最大值都远远超过了75%的数据，而在最小值到三分位之间的数据差异较为平均，不知道这些较大数对最终酒的质量有何种影响。
quality
fixed.acidity
双变量分析
分析散点矩阵的相关性系数：从散点矩阵观察，与quality相关系数比较大的数据有：quality与volatile.acidity的相关系数是-0.391, 与alcohol的相关系数是0.476,另外与sulphates相关系数是0.25。在双变量分析时，重点分析这些变量之间的关系。
从上图大致可看出，约有50%的酒质量集中在5，6之间，另外fixed.acidity近似于最大值16时质量是5，质量为7、8是，fiexed.acidity通常并不太高，大部分在13以下。
quality5-7之间的酒分布比较集中，也可以大致观察到，在quality<4的酒中，有一些volatile.acidity含量较高，而在>7的酒中，volatile.acidity的含量普遍较低一些.
上图大致趋势是，quality和volatile.acidity之间有一个递减关系。
### 在几个等级的酒的分布中，citric.acid分布都比较均匀。从中位数的折线图来看，有一定的递增关系。
## `geom_smooth()` using method = 'gam'
从上图大致分析，fixed.acidity 和density约为线性关系，density随fixed.acidity的增大而减小
从上图分析，fixed.acidity和pH值大约为线性关系，fixed.acidity越大，pH值越小。(这也符合逻辑，pH值就是用来衡量酸碱度的)
## `geom_smooth()` using method = 'gam'
density和alcohol大致为指数递减关系，二者相关系数是0.496
## `geom_smooth()` using method = 'gam'
total.sulfur.dioxide随free.sulfur.dioxide增大而增大，这也是符合逻辑的。总二氧化硫含量和剩余二氧化硫含量之间相关性很大，其他条件不变的情况下，剩余二氧化硫越多，总二氧化硫越多。
- 二氧化硫在酒中以气体形式存在，它的浓度影响酒的风味。
## Warning: Removed 15 rows containing non-finite values (stat_summary).
## `geom_smooth()` using method = 'gam'
##
## 4.6 4.7 4.9 5 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 6 6.1
## 1 1 1 6 4 6 4 5 1 14 2 4 9 13 16
## 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 7 7.1 7.2 7.3 7.4 7.5 7.6
## 20 14 25 17 37 28 46 38 50 57 67 44 44 52 46
## 7.7 7.8 7.9 8 8.1 8.2 8.3 8.4 8.5 8.6 8.7 8.8 8.9 9 9.1
## 49 53 42 42 26 45 40 26 19 27 24 34 33 26 29
## 9.2 9.3 9.4 9.5 9.6 9.7 9.8 9.9 10 10.1 10.2 10.3 10.4 10.5 10.6
## 16 22 17 14 17 9 15 26 23 10 19 11 21 12 14
## 10.7 10.8 10.9 11 11.1 11.2 11.3 11.4 11.5 11.6 11.7 11.8 11.9 12 12.1
## 10 10 8 3 9 5 7 5 13 12 3 3 12 7 1
## 12.2 12.3 12.4 12.5 12.6 12.7 12.8 12.9 13 13.2 13.3 13.4 13.5 13.7 13.8
## 4 5 4 7 4 4 5 2 3 3 3 1 1 2 1
## 14 14.3 15 15.5 15.6 15.9
## 1 1 2 2 2 1##
## 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.11 0.12 0.13 0.14
## 132 33 50 30 29 20 24 22 33 30 35 15 27 18 21
## 0.15 0.16 0.17 0.18 0.19 0.2 0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.28 0.29
## 19 9 16 22 21 25 33 27 25 51 27 38 20 19 21
## 0.3 0.31 0.32 0.33 0.34 0.35 0.36 0.37 0.38 0.39 0.4 0.41 0.42 0.43 0.44
## 30 30 32 25 24 13 20 19 14 28 29 16 29 15 23
## 0.45 0.46 0.47 0.48 0.49 0.5 0.51 0.52 0.53 0.54 0.55 0.56 0.57 0.58 0.59
## 22 19 18 23 68 20 13 17 14 13 12 8 9 9 8
## 0.6 0.61 0.62 0.63 0.64 0.65 0.66 0.67 0.68 0.69 0.7 0.71 0.72 0.73 0.74
## 9 2 1 10 9 7 14 2 11 4 2 1 1 3 4
## 0.75 0.76 0.78 0.79 1
## 1 3 1 1 1多个变量分析
## Warning: Removed 29 rows containing non-finite values (stat_summary).
酸性物质总量与pH值关系很大，但是没有直接显示出对红酒质量的影响。在红酒的几个质量等级中，酸性物质的含量大多在(5,15之间)，总pH值都在(3,4)之间.
线性预测模型
## [1] "X" "fixed.acidity" "volatile.acidity"
## [4] "citric.acid" "residual.sugar" "chlorides"
## [7] "free.sulfur.dioxide" "total.sulfur.dioxide" "density"
## [10] "pH" "sulphates" "alcohol"
## [13] "quality" "acid"## Loading required package: lattice## Loading required package: MASS##
## Attaching package: 'memisc'## The following objects are masked from 'package:stats':
##
## contr.sum, contr.treatment, contrasts## The following object is masked from 'package:base':
##
## as.array##
## Calls:
## model: lm(formula = I(acid ~ quality), data = wine)
## model2: lm(formula = acid ~ quality + fixed.acidity, data = wine)
## model3: lm(formula = acid ~ quality + fixed.acidity + volatile.acidity,
## data = wine)
## model4: lm(formula = acid ~ quality + fixed.acidity + volatile.acidity +
## citric.acid, data = wine)
## model5: lm(formula = acid ~ quality + fixed.acidity + volatile.acidity +
## citric.acid + alcohol, data = wine)
## model6: lm(formula = acid ~ quality + fixed.acidity + volatile.acidity +
## citric.acid + alcohol + sulphates, data = wine)
##
## ========================================================================================================================================================================================
## model model2 model3 model4 model5 model6
## ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
## (Intercept) 7.791*** 0.629*** -0.018 0.000*** 0.000** 0.000**
## (0.322) (0.031) (0.033) (0.000) (0.000) (0.000)
## quality 0.235*** -0.046*** -0.001 0.000* 0.000 0.000
## (0.056) (0.005) (0.004) (0.000) (0.000) (0.000)
## fixed.acidity 1.051*** 1.063*** 1.000*** 1.000*** 1.000***
## (0.002) (0.002) (0.000) (0.000) (0.000)
## volatile.acidity 0.556*** 1.000*** 1.000*** 1.000***
## (0.019) (0.000) (0.000) (0.000)
## citric.acid 1.000*** 1.000*** 1.000***
## (0.000) (0.000) (0.000)
## alcohol 0.000 0.000
## (0.000) (0.000)
## sulphates 0.000
## (0.000)
## ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
## R-squared 0.011 0.993 0.996 1.000 1.000 1.000
## adj. R-squared 0.010 0.993 0.996 1.000 1.000 1.000
## sigma 1.823 0.151 0.122 0.000 0.000 0.000
## F 17.379 116247.523 118938.541 2674897743917158941414433751040.000 2138865031038253163413986344960.000 1781348751094982461809856872448.000
## p 0.000 0.000 0.000 0.000 0.000 0.000
## Log-likelihood -3228.395 751.025 1092.088 47989.920 47990.028 47990.064
## Deviance 5309.616 36.594 23.886 0.000 0.000 0.000
## AIC 6462.791 -1494.050 -2174.177 -95967.839 -95966.056 -95964.128
## BIC 6478.922 -1472.541 -2147.291 -95935.577 -95928.416 -95921.111
## N 1599 1599 1599 1599 1599 1599
## ========================================================================================================================================================================================最终图像
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反思：
- 这个数据集包含1599条红酒数据，质量变量是一个离散型变量，在研究其他变量对质量的影响时，散点图用的比较多。
- 分析变量之间的关系时用到的思路比较少，有时会不知道从哪里入手。
- 完成此项目时从google,wiki等网站查阅了关于红酒化学成分的一些资料。
- 从分析到建立模型到预测的过程有些不太清楚。